On irrationality of some distances between points on a circle

Mladen Vassilev–Missana
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 4—9
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Authors and affiliations

Mladen Vassilev–Missana
5 Victor Hugo Str, Ap. 3
1124 Sofia, Bulgaria

Abstract

Let n > 3 be arbitrary integer. In the present paper it is shown that if K is an arbitrary circle and Mi, i = 1,…,n are points on K, dividing K into n equal arcs, then for each point M on K, different from the mentioned above, at least of the distances |MMi| are irrational numbers.

Keywords

  • Distance
  • Irrational number
  • Circle

AMS Classification

  • 97G40
  • 11XX

References

  1. Coolidge, J. L. (1939) A Historically Interesting Formula for the Area of a Quadrilateral. Amer. Math. Monthly, 46, 345–347.
  2. Nagell, T. (1951) Introduction to Number Theory. Wiley, New York.
  3. Mason, J. C., & Handscomb, D. C. (2003) Chebyshev Polynomials. CRC Press, New York.

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Cite this paper

APA

Vassilev–Missana, M. (2016). On irrationality of some distances between points on a circle. Notes on Number Theory and Discrete Mathematics, 22(2), 4-9.

Chicago

Vassilev–Missana, Mladen. “On Irrationality of Some Distances between Points on a Circle.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 4-9.

MLA

Vassilev–Missana, Mladen. “On Irrationality of Some Distances between Points on a Circle.” Notes on Number Theory and Discrete Mathematics 22.2 (2016): 4-9. Print.

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